arXiv subjects

Luis Sánchez-González

Publications and source records attributed to Luis Sánchez-González.

3 recordsLinked to original sources

arXiv2014

Low distortion embeddings into Asplund Banach spaces

We give a simple example of a countable metric space $M$ that does not embed bi-Lipschitz with distortion strictly less than 2 into any Asplund space. Actually, if $M$ embeds with distortion strictly less than 2 to a Banach space $X$, then $X$ contains an isomorphic copy of $\ell_1$. We also show that the space $M$ does not embed with distortion strictly less than $2$ into $\ell_1$ itself but it does embed isometrically into a space that is isomorphic to $\ell_1$.

math.FA↗

arXiv2014

Low distortion embeddings between $C(K)$ spaces

We show that, for each ordinal $α<ω_1$, the space $C([0,ω^α])$ does not embed into $C(K)$ with distortion strictly less than $2$ unless $K^{(α)}\neq \emptyset$.

math.FA↗

arXiv2013

Global inversion of nonsmooth mappings using pseudo-Jacobian matrices

We study the global inversion of a continuous nonsmooth mapping $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f, introduced by Jeyakumar and Luc, and we consider a related index of regularity for f. We obtain a characterization of global inversion in terms of its index of regularity. Furthermore, we prove that the Hadamard integral condition has a natural counterpart in this setting, providing a sufficient condition for global invertibility.

math.FA↗